If P = 1 α 3 1 3 3 2 4 4 is the adjoint of a 3 × 3 matrix A and A = 4 , then α is equal to

Question

If P = 1 α 3 1 3 3 2 4 4 is the adjoint of a 3 × 3 matrix A and A = 4 , then α is equal to, 5, 0, 4, 11

MARKS App · Accepted Answer

Given P = a d j A ⇒ P = a d j A = A 2 ∵ a d j A = A n - 1 where n = 3 Now, P = 1 α 3 1 3 3 2 4 4 = 1 × 12 − 12 − α × 4 − 6 + 3 × 4 − 6 = 2 α - 6 ⇒ 2 α - 6 = 1 6 ⇒ α = 11

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